1. Introduction and a short review on magnetism

• „Quantum“ vs. „classical“ magnetism
• Bohr – van Leeuwen Theorem
• Magnetism of free atoms
• Link: Images representing atomic orbitals
• Hund‘s rules, spin-orbit coupling
• Magnetism in solids
• Cooperative phenomena
• Hubbard model, kinetic exchange

2. Molecular magnets: 0D quantum magnets

• Link: MolMag web - a link to molecular magnetism
• Comprehensive Literature: Book Molecular Nanomagnetism by Gatteschi, Sessoli, Villain (link via HEIDI)
• What is a molecular magnet?
• Spin Hamiltonian, uniaxial and in-plane anisotropy
• Slow relaxation
• Quantum Tunnelling of the Magnetization
• Ni2, Mn12, Fe8, Mn4, Mn2Ni3
• micro-Hall and micro-SQUID magnetometry
• ESR on molecular magnets
• Molecular Q-Bits, spin coherence, dephasing

3. 1D quantum magnets

• Educational review on spin liquids (in German): Das Wechselspiel magnetischer Anregungen in Spinflüssigkeiten (Uhrig, Grüninger) Link via Physik Journal DPG
• Non-interacting dimers
• RVB state
• Mermin-Wagner theorem
• For experts: Theory tutorial by H. Wagner, U. Schollwoeck on the MW theorem (Link to schlarpedia)
• Uniform AFM 1D Heisenberg chain
• Inelastic Neutron Scattering
• S=1 Haldane chain
• Link: Haldane, PRL 1983 (Link to PRL)
• 1D heat transport
• Anisotropic Heisenberg chain
• Alternating Heisenberg chain
• Spin-Peierls transition
• Spin ladders
• Advanced further reading: M. Imada, A. Fujimori, Y. Tokura: Metal-Insulator transitions, Rev. Mod. Phys. 70, 1039–1263 (1998) (Link to RMP)

4. Quantum magnets in external magnetic field

• Isolated dimers vs. coupled dimers
• uniform HAF
• "Bose-Einstein condensation of magnons"

5. Geometrically frustrated magnets

• Geometric magnetic frustration
• Spin ice
• Further reading: Pauling 1935: The structure and entropy of ice... (Link to JACS)
• Further reading: Gingras 2009: Observing Monopoles in a Magnetic Analog of Ice (Link to Science magazine)
• Further reading: Review, Science 2001 (Link to Science magazien)
• Magnetic monopoles
• Spin and orbital frustration
• Frustrated quantum spin chains (reminder)
• Magnetic refridgeration

5.  2D quantum magnets

• Topological defects
• Kosterlitz-Thouless transition
• Link: Nobel Prize in Physics 2016 for Kosterlitz, Thouless, and Haldane
• Zhang-Rice Singlets
• Hole-doped spin ladders
• 2D Heisenberg AFM
• Cuprate superconductors
• Link: The Nobel Prize in Physics 1987
• Stripes